I've been battling this for almost a month now. My installer is also confused and Garmin hasn't been much help either. I have a 750xi, GI275 ADAHRS, and a GFC500 AP. I'll try and keep this short and sweet :-)
Initial systems ops check flight - ILS: 750xi auto switches from GPS to VLOC (indicated at the bottom of the 750xi) but the 275's don't auto switch. They do however flash the "CDI" button at me indicating I need to manually switch. **Pictures 1 & 3 show CDI button (750xi), VLOC, and flashing "CDI" on the 275's**
Then my installer calls Garmin... Garmin tells them to deactivate the CDI button on the 750xi. I now have lost my "ILS CDI Auto Capture" button in the settings of the 750xi and the CDI button is gone from the bottom of the 750xi. Also, you can see on the ADI that "LOC" and "GS" are armed, but yet it never captured them. **Picture 2**
Second ILS attempt - Airplane flies right through final. No flashing CDI button on the 275's either. As soon as I hit the CDI button on the bottom of my HSI or CDI (I have both), it grabs the ILS and turns me towards final. In the maintenance manual, you can turn the CDI button back to active, which will give you the "auto switch" option back under "ILS CDI Auto Capture." I'm starting to think the configuration of the 275's is my problem. I've found several videos demoing this, so I know it's capable, but the correct way to set this up appears to be a mystery. I'll let you know more if we ever get it figured out...
